Problem preview
G-GPE.4 Warmup M2-043-A04-V01

Use coordinates to prove simple geometric theorems, including simple circle theorems.

Compare midpoint coordinates to verify bisection

Problem

Do segments \(AC\) and \(BD\) bisect each other? Use midpoint coordinates to decide: \(A(0,0)\), \(C(6,8)\), \(B(2,7)\), \(D(4,1)\).

Big Picture

What this problem is really about

Intersection alone does not prove bisection; the meeting point must halve both segments. We’ll calculate each midpoint independently by averaging both endpoint coordinates, compare the complete ordered pairs, and use opposite displacement vectors from the common point as a final check that both segments are split into equal halves.

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Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-GPE.4
Category
Geometry
Domain
Expressing Geometric Properties with Equations
Objective
Use coordinates to prove simple geometric theorems, including simple circle theorems.
Problem type
Compare midpoint coordinates to verify bisection